Theoretical research will be conducted on the properties of the two-dimensional electron liquid in the presence of long-range disorder. This type of disorder is usually created in heterostructures with large spacer width by randomly distributed remote impurity ions. Screening by the two-dimensional electron liquid competes effectively with the resultant random potential. However, in some cases this screening is not effective and the two- dimensional electron liquid becomes very inhomogeneous. In a strong magnetic field this state occurs each time the filling factor of the Landau level corresponds to an integer or a fractional gap. Different manifestations of the inhomogeneous state will be studied: the low temperature behavior of the conductivity tensor in the filling factor range where all gaps are destroyed by disorder; the width of the plateau of the quantum Hall effect; the attenuation of the surface acoustic waves; the Wigner crystal formation in the presence of the long range disorder. %%% Theoretical studies will be made on the physics of mesoscopic systems where quantum effects are manifest on a macroscopic scale. In particular, studies will be made on the effects of disorder on the properties of the two-dimensional electron liquid which forms at junctions between semiconductors.
